document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074311>Question 1074311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A courier service  promises that 80% of deliveries will reach their destinations within 12 hours.what is the probability that of the 7 parcels sent at random times  only one is delivered late? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689005 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> binomial formula is p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "p is the probability of occurrence.<BR>\n" );
document.write( "p is the probability of no occurrence = 1 - p.<BR>\n" );
document.write( "x is the number of occurrences.<BR>\n" );
document.write( "(n-x) is the number of non-occurrences.<BR>\n" );
document.write( "c(n,x) is the combination formula for number of ways you can get x out of n without regard to order.\r<BR>\n" );
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document.write( "the probability of occurrence here would be the probability that the package is being delivered late.\r<BR>\n" );
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document.write( "since 80% arrive within 12 hours, then 20% must not arrive within 12 hours.\r<BR>\n" );
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document.write( "therefore, p = .2 and q = .8\r<BR>\n" );
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document.write( "p means the probability the package will be late.<BR>\n" );
document.write( "q means the probability the paqckage will be on time.\r<BR>\n" );
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document.write( "if at least 6 out of 7 arrive on time, this means that at most 1 arrives late.\r<BR>\n" );
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document.write( "this means that either 0 arrive later or 1 arrives late.\r<BR>\n" );
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document.write( "therefore, you want p(0) + p(1).\r<BR>\n" );
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document.write( "p(0) = .2^0 * .8^7 * c(7,0) = 1 * .2097152 * 1 = .2097151<BR>\n" );
document.write( "p(1) = .2^1 * .8^6 * c(7,1) = .2 * .262144 * 7 = .3670016\r<BR>\n" );
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document.write( "the total probability of p(0) + p(1) = .5767526\r<BR>\n" );
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document.write( "the following pictures shows all the probabilities from x = 0 to x = 7\r<BR>\n" );
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document.write( "their sum has to be equal to 1, as it is.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032601.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the numbers shown for p(1) and p(2) are rounded a little more than the numbers i showed you above, but they are the same numbers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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